How to Leak a Key

It’s been been interesting following the great Heartbleed crisis over the last week. The “Heartbleed Challenge” set up by Cloudflare established that you could get the server private key, specifically, the primes used to generate the key would show up in the Heartbleed data occasionally. Doing a memory dump of a simple OpenSSL server application (https://github.com/matthewarcus/ssl-demo) showed that after reading the keys at startup, it later copies the prime data to higher locations in the heap where they become more likely to be included in a Heartbeat response.

An extract from a hex dump of the heap after making a single request shows:

The first line in each section is the malloc header, the second line is part of the data; also, all of these malloced blocks are in use (otherwise some of the data would be overwritten with free list data).

The first two primes are from the initial processing of the private key, the next two items are the input and output buffers for the connection, then we have two more copies of the primes, which only appear after a connection has been made.

So where are these persistent copies of the primes coming from? Some investigation shows that the first time OpenSSL actually uses an RSA key for a private operation, it calculates various auxiliary values for use in Montgomery arithmetic and stores them away in the key structure. Unfortunately, one of the values that gets stored away is the modulus used, which in this case is one of the primes:

That BN_copy in the last line is the culprit. Once allocated, these values stay in memory until the RSA key is deleted. So even if the original key data is stored in protected or hard to get at memory, a Heartbleed attack may still be able to get to the primes.

This also explains why, as far as I know, no one has managed to capture the CRT parameters or the private exponent itself – they stay safely tucked away in the low part of the heap. Also, depending on the application startup behaviour, it might be that the primes end up below the input buffers (by default, OpenSSL caches up to 32 previously allocated buffers of each type) in which case they won’t be visible to Heartbleed – this might explain why in the Cloudflare challenge, only one of the primes seemed to be turning up.

Update 20/04/14: actually, it’s worse than this – bignum resizing can also leak private data onto the heap in unpredictable ways, more details to follow.